How to integrate int 1/(1+x^3)dx ?

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The integral of 1/(1+x^3) dx can be expressed as (1/3) ln(x+1) - (1/6) ln(x^2 - x + 1) + (1/2) ∫(1/(x^2 - x + 1)) dx. The discussion highlights the challenge of solving the remaining integral ∫(1/(x^2 - x + 1)) dx. Participants are encouraged to provide solutions or methods to tackle this specific integral.

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Alexx1
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I try to solve the integral 1/(1+x^3) dx , but I got stuck

Now I got as solution:

(1/3) ln(x+1) - (1/6) ln(x^2 -x+1) + (1/2) integral (1/(x^2 -x+1))

Can someone help me to solve the last integral? I have absolutely no idea how I can solve that one..

So integral: 1/(x^2 -x+1) dx
 
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